Yeah there is a word for treating eachother with friendship - "friends". Being friendly. This is already included in social skills.
The company saying they want to be family is super annoying to me. It's a JOB, not a personal relationship you choose yourself. Saying it's a family implies you should feel loyalty to the company, when in fact, it's a business relationship.
They are trying to blur the lines by saying family and its complete bullshit. I wouldn't even have a job if they didn't give me money for it, but I would have a family. See the crystal clear difference?